Lisa_special number groups

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Published on December 1, 2008

Author: lisamahon

Source: authorstream.com

Slide 1: Special number groups By Lisa Mahon Slide 2: Arithmetic Sequences An Arithmetic Sequence is made by adding some value each time. This sequence has a difference of 3 between each number. The pattern is continued by adding 3 to the last number each time. This sequence has a difference of 5 between each number. The pattern is continued by adding 5 to the last number each time. Activity: In your work booklet make a sequence that starts at 5 and increases by 6 Slide 3: Geometric Sequences A Geometric Sequence is made by multiplying by some value each time. This sequence has a factor of 2 between each number.The pattern is continued by multiplying the previous number by 2 each time. This sequence has a factor of 3 between each number.The pattern is continued by multiplying the last number by 3 each time. Activity: In your work booklet make up your own Geometric sequence Slide 4: Even Numbers Activity: Complete the questions in your the work booklet Slide 5: Odd Numbers Activity: Complete the questions in your booklet Slide 6: 1 x 1 = 1     1 is a square number 2 x 2 = 4     4 is a square number 3 x 3 = 9     9 is a square number 4 x 4 = 16    16 is a square number 5 x 5 = 25    25 is a square number 6 x 6 = 36    36 is a square number 7 x 7 = 49    49 is a square number 8 x 8 = 64    64 is a square number 9 x 9 = 81    81 is a square number 10 x 10 = 100    100 is a square number 11 x 11 = 121     121 is a square number 12 x 12 = 144    144 is a square number 13 x 13 = 169    169 is a square number 14 x 14 = 196    196 is a square number 15 x 15 = 225    225 is a square number and so on Square Numbers Slide 7: Activity: Complete the questions in your work booklet before going to next slide Slide 8: You have just learnt what a square number is. By looking at the pattern below in your own words write a definition for a cubed number? 1 x 1 x 1 = 1     1 is a cubed number 2 x 2 x 2= 8     8 is a cubed number 3 x 3 x 3= 27     27 is a cubed number 4 x 4x 4 = 64     64 is a cubed number 5 x 5 x 5 = 125    125 is a cubed number 6 x 6 x 6 = 216    216 is a cubed number 7 x 7 x 7= 343    343 is a cubed number 8 x 8 x 8= 512     512 is a cubed number 9 x 9 x 9= 729    729 is a cubed number  etc Activity: Complete the questions in your work booklet before going to next slide Cubed Numbers Slide 9: Cube Numbers Therefore the sequence for cubed numbers are: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 etc Slide 10: 2 only divides by 1 and 2          2 is a prime number3 only divides by 1 and 3          3 is a prime number5 only divides by 1 and 5          5 is a prime number7 only divides by 1 and 7          7 is a prime number 11 only divides by 1 and 11       11 is a prime number13 only divides by 1 and 13      13 is a prime number17 only divides by 1 and 17      17 is a prime number19 only divides by 1 and 19      19 is a prime number 23 only divides by 1 and 23     23 is a prime number29 only divides by 1 and 29     29 is a prime number 31 only divides by 1 and 31      31 is a prime number37 only divides by 1 and 37     37 is a prime number41 only divides by 1 and 41      41 is a prime number43 only divides by 1 and 43     43 is a prime number47 only divides by 1 and 47     47 is a prime number 53 only divides by 1 and 53     53 is a prime number59 only divides by 1 and 59     59 is a prime number and so on Prime Numbers in Mathematics Activity: Complete the questions a (a) and (b) in your work booklet before going to next slide Slide 11: A prime number is a number with exactly two factors, which are one (1), and itself. 2 has the factors 1 and 2; 3 has the factors 1 and 3; 5 has the factors 1 and 5; 11 has the factors 1 and 11 Numbers which are not prime are called composite numbers. Slide 12: Factors A factor is “something which will divide a number exactly”. Cambridge dictionary Activity: Write the definition of a factor in work booklet Slide 13: The factors of 7 are 1 and 7 because 7 x 1 = 7 The factors of 12 are 1, 2, 3, 4, 6 and 12 because 1 x 12 = 12 2 x 6 = 12 3 x 4 = 12 To find the factors of a number, list all the possibilities first, then list the numbers from smallest to largest. 1 x 48 = 48 2 x 24 = 48 3 x 16 = 48 4 x 12 = 48 6 x 8 = 48 The factors of 48 are 1,2,3,4,6,8,12,16,24,48 Before continuing, complete questions in work booklet for factors Slide 14: Common Factors The common factors of 4 and 6 are 1 and 2 since 1 and 2 are factors of both 4 and 6 The common factors of 8 and 24 are 1, 2, 4 and 8 since 1, 2, 4 and 8 are factors of both 8 and 24 Slide 15: Highest Common Factors In the above example 2 is the HCF In the above example 8 is the HCF Slide 16: If you find all the factors of two or more numbers, and you find some factors are the same (common), then the largest of those common factors is the Highest Common Factor (HCF) What is the Highest Common Factor? Complete the questions in your booklet for HCF before moving to next slide Slide 17: Multiples 3 times tables 3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18 3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 30 3 x 11 = 33 3 x 12 = 36 3 x 13 = 39 3 x 14 = 42 3 x 15 = 45 3 x 16 = 48 etc These are multiples The product of a given whole number and another whole number What are Multiples? Slide 18: Therefore the multiples of 3 are: 3, 6, 9, 12,1 5, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51 etc. That is, the answers to your 3 times tables Go to the next slide and complete the question and activities in your work booklet Slide 19: Multiples of 5 On your worksheet shade the remaining multiples of 5 Slide 20: Multiples of 7 On your worksheet shade the remaining multiples of 7 Slide 21: Multiples of 10 On your worksheet shade the remaining multiples of 10 Slide 22: Have you noticed that multiples are simply the answers to your times tables? Slide 23: Lowest Common Multiple The smallest common multiple of two or more numbers is called the lowest common multiple (LCM). For Example: Find the LCM 6 and 9? 6 12 18 24 30 36 42 First, list the multiples of 6 and 9 9 18 27 36 45 54 63 Then, look at both columns of number and find the first common number Answer: LCM is 18 In your work booklet, complete the questions and activity Slide 24: Triangular numbers, 1, 3, 6, 10, 15, 21 . . . which are generated by 1, 1+2, 1+2+3, 1+2+3+4, 1+2+3+4+5, 1+2+3+4+5+6 . . . . They are called triangular numbers because you can make them up into neat triangles like this: Triangular Numbers Image: www.shyamsundergupta.com/triangle.gif Slide 25: There are several really cute things about these numbers that were known, way back in the days of Diophantus, an Ancient Greek who liked playing with really big numbers. One Example: Every perfect square is the sum of two consecutive triangular numbers, 1 + 3 = 4 = 22 3 + 6 = 9 = 32 A Triangular number can never end in 2, 4, 7 or 9: Another Example: Slide 26: What is a Palindromic Number? Numbers that read the same backwards as forwards. Examples are 11, 123321 and 2002. Palindromic is the number equivalent of a Palindrome which is a word which reads the same forwards and backwards. For example. Hannah Palindromic Number Slide 27: Fibonacci numbers are the elements of the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765 . . . Sometimes this sequence is given as 0, 1, 1, 2, 3, 5 . . . (0 becomes the 0th element of the sequence). Each number is the sum of the two previous numbers. There are other Fibonacci sequences, starting with other numbers: 3, 10, 13, 23, 36, 59 . . . Fibonacci numbers Fibonacci numbers is named after the 13th Century mathematician, Leonardo of Pisa, also called Leonardo Fibonacci

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